3x+7/(x-1)(x-2)=A/(x-1)+B/(x+2),
右边通分=[A(x+2)+B(x-1)]/(x-1)(x-2)
=[(A+B)x+(2A-B)]/(x-1)(x-2)
=(3x+7)/(x-1)(x-2)
所以(A+B)x+(2A-B)=3x+7
所以A+B=3
2A-B=7
相加
3A=10
A=10/3
B=3-A=-1/3